F(n) is the n-th Fibonacci number.

PFGW Version 1.2.0 for Windows [FFT v23.8]

Primality testing 52160*F(52160)+1
[N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 13
Running N-1 test using base 17
Running N+1 test using discriminant 31, base 15+sqrt(31)
52160*F(52160)+1 is Fermat and Lucas PRP!

To be completed...